Finite Group Databasebeta

← #14289986

Subgroups — #14289986

Order 1920.

424 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756344C211yesmaximal, characteristic
2C5×#5020C211yesmaximal, characteristic, complemented
3#11747105C211yesmaximal, characteristic, complemented
4#11746912C211yesmaximal, characteristic
5C3×Q8⋊#168C211yesmaximal, characteristic, complemented
6#11745854C211yesmaximal, characteristic
7#11745845C211yesmaximal, characteristic, complemented
8#10601921—31nomaximal, Hall
9C3×C4×C5×Q8C2211yescharacteristic
10#91836—21no—
11#91783—22no—
12#91782—21no—
13#91764—21no—
14#91763C2211yescharacteristic
15C4×D60—21no—
16C4×Dic30C2211yescharacteristic
17C5×#869C2211yescharacteristic
18C2×#6663—21no—
19C5×#835—21no—
20C5×#808—21no—
21C5×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×C4⋊#168C2211yescharacteristic
23C3×C4×#168C2211yescharacteristic
24#90973—21no—
25#90969—22no—
26#68254—51nomaximal, Hall
27#65919—31no—
28C5×#475—31no—
29#65379—31no—
30#65377—31no—
31Q8⋊#168D311yescharacteristic, complemented
32#64705—31no—
33#64704—31no—
34C2×C3×C5×Q8D411yescharacteristic
35C2×D60—21no—
36C2×D60—21no—
37C2×D60D412yes—
38C2×C4×D15—22no—
39C2×Dic30D411yescharacteristic
40C2×C5×Dic6—21no—
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4D411yescharacteristic
43C3×C42×C5—21no—
44C3×C42×C5C2311yescharacteristic
45#6714—22no—
46#6714—22no—
47#6714—22no—
48C4⋊Dic15D411yescharacteristic
49#6712—21no—
50C4×Dic15—21no—
51C5×C4⋊Dic3—21no—
52C5×C4⋊Dic3—21no—
53C2×C5×C3⋊C8—21no—
54C2×C3×#168—21no—
55C2×C3×#168—21no—
56#6663—42no—
57#5585—51no—
58#5020D511yescharacteristic, complemented
59#4849—51no—
60#4694—51no—
61C3×Q8⋊C8—51no—
62#4485—51no—
63#4456—51no—
64C5×C4⋊Q8—31no—
65C4×C5×Q8C2×D311yescharacteristic
66#4093—61no—
67C2×#689—61no—
68#4040—62no—
69#4039—61no—
70#4021—61no—
71#4020—31no—
72C4×D20—61no—
73C4×Dic10—31no—
74C5×#106—61no—
75C5×C4⋊C8—31no—
76C5×#103—61no—
77#3967—61no—
78#3941—62no—
79C4⋊#168C2×D311yescharacteristic
80C4×#168C2×D311yescharacteristic
81#1640—151noSylow
82C22×D15—22no—
83C3×C5×Q8—21no—
84C3×C5×Q8—21no—
85C2×C3×C4×C5—21no—
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×Dic15—21no—
91C2×Dic15—21no—
92D60—42no—
93D60—41no—
94D60—41no—
95D60—41no—
96D60—41no—
97C4×D15—82no—
98Dic30—21no—
99Dic30—21no—
100C2×C5×Dic3—41no—
101C5×Dic6—41no—
102C5×Dic6—41no—
103C3×#168—41no—
104C3×#168—41no—
105C5×C3⋊C8—41no—
106C3×C4×Q8C2×D511yescharacteristic
107#947—101no—
108C2×Dic12—101no—
109#894—102no—
110#893—101no—
111#875—101no—
112#874—51no—
113C4×D12—101no—
114#869C2×D511yescharacteristic
115C4×Dic6—51no—
116C3×C4⋊C8—51no—
117C3×C4×C8—51no—
118#835—21no—
119#821—102no—
120#816—101no—
121#808—21no—
122C4⋊(C3⋊C8)C2×D511yescharacteristic
123C2×C5×Q8—61no—
124C2×C5×Q8D1211yescharacteristic
125C2×D20—32no—
126C2×D20—61no—
127C2×D20—61no—
128C2×C4×D5—62no—
129C2×Dic10—31no—
130C2×C5×C8—61no—
131C5×C4⋊C4—21no—
132C5×C4⋊C4—61no—
133C5×C4⋊C4—61no—
134C5×C4⋊C4D1211yescharacteristic
135C42×C5—21no—
136C42×C5C22×D311yescharacteristic
137#689—122no—
138#685—62no—
139#685—62no—
140#685—62no—
141C4⋊Dic5—31no—
142#683—61no—
143C4×Dic5—61no—
144C2×#168—21no—
145C2×#168—21no—
146#559—151no—
147#486—151no—
148#475—31no—
149#462—151no—
150#331—151no—
151Q8⋊C8—51no—
152Q8⋊C8—151no—
153C22×C3×C5#12011yescharacteristic
154C2×D15—42no—
155C2×D15—42no—
156C2×D15—42no—
157C3×C4×C5—21no—
158C3×C4×C5—41no—
159C3×C4×C5—41no—
160C3×C4×C5#13511yescharacteristic
161C3×C4×C5#13511yescharacteristic
162C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
163C3×C4×C5#13711yescharacteristic
164Dic15—41no—
165Dic15—41no—
166C5×Dic3—81no—
167C2×C3×Q8C22⋊D511yescharacteristic
168C2×D12—52no—
169C2×D12—101no—
170C2×D12—101no—
171C2×C4×D3—102no—
172C2×Dic6—21no—
173C2×Dic6—51no—
174C2×C3×C8—101no—
175C2×C3×C8—101no—
176C3×C4⋊C4—21no—
177C3×C4⋊C4C22⋊D511yescharacteristic
178C3×C42—21no—
179C3×C42C22×D511yescharacteristic
180(C2×D3)⋊C4—102no—
181(C2×D3)⋊C4—102no—
182(C2×D3)⋊C4—102no—
183C4⋊Dic3—21no—
184C4⋊Dic3—21no—
185C4⋊Dic3—51no—
186Dic3⋊C4—101no—
187C4×Dic3—101no—
188C2×C3⋊C8—21no—
189Dic12—202no—
190C22×D5—62no—
191C5×Q8—21no—
192C5×Q8—21no—
193C5×Q8—121no—
194C5×Q8—121no—
195C2×C4×C5—21no—
196C2×C4×C5—21no—
197C2×C4×C5—121no—
198C2×C4×C5C2×D1211yescharacteristic
199C2×C4×C5D3×D411yescharacteristic
200C2×C4×C5D3×D411yescharacteristic
201C2×Dic5—61no—
202C2×Dic5—61no—
203D20—122no—
204D20—121no—
205D20—121no—
206D20—121no—
207D20—121no—
208C4×D5—242no—
209Dic10—61no—
210Dic10—61no—
211C5×C8—121no—
212#168—41no—
213#168—41no—
214C2×Q16—301no—
215C4⋊Q8—31no—
216#127—151no—
217#124—301no—
218#124—301no—
219#123—302no—
220C4×Q8—151no—
221C4×Q8D3×D511yescharacteristic
222C4×D4—301no—
223C4×D4—301no—
224#106—61no—
225C4⋊C8—31no—
226C4⋊C8—51no—
227#103—61no—
228#103—301no—
229#102—302no—
230C4×C8—51no—
231C2×C3×C5#44911yescharacteristic
232C2×C3×C5#45211yescharacteristic
233C2×C3×C5#45511yescharacteristic
234D15—82no—
235C22×D3—102no—
236C3×Q8—21no—
237C3×Q8—21no—
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4D4×D511yescharacteristic
241C2×C3×C4D4×D511yescharacteristic
242C2×C3×C4C2×C22⋊D511yescharacteristic
243C2×Dic3—41no—
244C2×Dic3—101no—
245C2×Dic3—101no—
246D12—202no—
247D12—201no—
248D12—201no—
249D12—201no—
250D12—201no—
251C4×D3—402no—
252Dic6—41no—
253Dic6—41no—
254Dic6—101no—
255Dic6—101no—
256C3×C8—201no—
257C3×C8—201no—
258C3⋊C8—41no—
259C22×C5#88211yescharacteristic
260C2×D5—122no—
261C2×D5—122no—
262C2×D5—122no—
263C4×C5—21no—
264C4×C5—41no—
265C4×C5—41no—
266C4×C5—241no—
267C4×C5#90411yescharacteristic
268C4×C5#90911yescharacteristic
269C4×C5#91411yescharacteristic
270C4×C5#91911yescharacteristic
271Dic5—121no—
272Dic5—121no—
273C2×Q8—61no—
274C2×Q8—151no—
275C2×Q8#120311yescharacteristic
276C2×D4—152no—
277C2×D4—301no—
278C2×D4—301no—
279C22×C4—302no—
280Q16—602no—
281C2×C8—61no—
282C2×C8—101no—
283C2×C8—101no—
284C4⋊C4—21no—
285C4⋊C4—61no—
286C4⋊C4—61no—
287C4⋊C4—151no—
288C4⋊C4—301no—
289C4⋊C4#120311yescharacteristic
290C22⋊C4—302no—
291C22⋊C4—302no—
292C22⋊C4—302no—
293C42—21no—
294C42—301no—
295C42C2×D3×D511yescharacteristic
296C3×C5#164011yescharacteristic, complemented, Hall
297C22×C3#408311yescharacteristic
298C2×D3—202no—
299C2×D3—202no—
300C2×D3—202no—
301C3×C4—21no—
302C3×C4—41no—
303C3×C4—41no—
304C3×C4#406011yescharacteristic
305C3×C4#406211yescharacteristic
306C3×C4#408811yescharacteristic
307C3×C4#409611yescharacteristic
308Dic3—81no—
309Dic3—201no—
310Dic3—201no—
311C2×C5#473311yescharacteristic
312C2×C5#481011yescharacteristic
313C2×C5#482511yescharacteristic
314D5—242no—
315C23—302no—
316Q8—21no—
317Q8—21no—
318Q8—121no—
319Q8—121no—
320Q8—301no—
321Q8—301no—
322D4—602no—
323D4—601no—
324D4—601no—
325D4—601no—
326D4—601no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—121no—
330C2×C4—301no—
331C2×C4—301no—
332C2×C4—1202no—
333C2×C4C2×#120311yescharacteristic
334C2×C4#679011yescharacteristic
335C2×C4#679011yescharacteristic
336C8—121no—
337C8—201no—
338C8—201no—
339C2×C3#6533611yescharacteristic
340C2×C3#6546111yescharacteristic
341C2×C3#6549111yescharacteristic
342D3—402no—
343C5#6825411yescharacteristic, complemented, Sylow
344C22—602no—
345C22—602no—
346C22—602no—
347C22#9157311yescharacteristic
348C4—21no—
349C4—41no—
350C4—41no—
351C4—241no—
352C4—601no—
353C4—601no—
354C4#9130311yescharacteristic
355C4#9132111yescharacteristic
356C4#9150611yescharacteristic
357C4#9152311yescharacteristic
358C3#1060192111yescharacteristic, complemented, Sylow
359C2—1202no—
360C2#1174856611yescharacteristic
361C2#1174928911yescharacteristic
362C2#1174946811yescharacteristic
subgroupG/H
centerC22#91573
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5#120
prime radical#91763C22
hypercenterC4×Q8D3×D5
hypocenterC3×C5#1640
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C5×#5020C2semidirect
3. #11747105C2semidirect
5. C3×Q8⋊#168C2semidirect
7. #11745845C2semidirect
31. Q8⋊#168D3semidirect
58. #5020D5semidirect
296. C3×C5#1640semidirect
343. C5#68254semidirect
358. C3#10601921semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#117563442
C5×#50202
#117471052
#117469122
C3×Q8⋊#1682
#117458542
#117458452
#106019213
#682545